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Probability

As reported by Runner's World magazine, the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Let X be the finishing time for a finisher in the New York 10-km run.
a) What is the chance that finishers complete the run with the times between 50 and 70 minutes?
b) What is the chance that finishers complete the run with the times more than 75 minutes?
c) How fast do finishers have to complete the run among the top 5% finishers?

Solution Preview

mu = 61, sigma = 9

(a) x = 50

z = (x - mu)/sigma = (50 - 61)/9 = -1.2222

x = 70

z = (x - mu)/sigma = ...

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